Abstracts

This paper provides a new model-free indicator of liquidity, the so-called LIX index. The computation of the LIX combines the recently developed conic finance theory which is built upon the concept of indices of acceptability with the option payoff spanning formula allowing for the extraction of the model-free asset distribution. The conic finance theory drops the law of one equilibrium price in favor of a two-price economy where market participants buy from the market at the ask price and sell to the market at the lower bid price. Under the framework of indices of acceptability, parametric expressions of the bid and ask prices of financial instruments can be obtained in terms of the distribution function of the zero cost cash-flow only. Matching the conic bid and ask prices of the stock with those observed in the market allows us to derive a model-free and unit-less indicator of spot liquidity. Just as the VIX and the SKEW index issued by the CBOE quantify the volatility and the tail risk perceived by today's investors, the resulting LIX index measures, in a similar market-implied fashion, the liquidity risk. Besides, we extend the methodology to build the so-called implied liquidity surfaces, one for the call and one for the put options, summarizing the dependency of the option model-free liquidity across moneyness and time to maturity. As numerical study, we provide a maximum likelihood estimation of popular mean-reverting processes applied to the time series of the new model-free liquidity proxy for vanilla options and their underlying, allowing for a comparison of the dynamics of liquidity in the underlying and derivative markets, but also during periods characterized by different market fear levels.